Acoustic resonances and trapped modes in pipes and tunnels

2008 ◽  
Vol 605 ◽  
pp. 401-428 ◽  
Author(s):  
STEFAN HEIN ◽  
WERNER KOCH
Keyword(s):  
Cross Sections ◽  
High Speed ◽  
Hard Spheres ◽  
Cutoff Frequency ◽  
Three Dimensional ◽  
Absorbing Boundary Conditions ◽  
Trapped Modes ◽  
Absorbing Boundary ◽  
Complex Scaling Method ◽  
Acoustic Resonances

Acoustic resonances of simple three-dimensional finite-length structures in an infinitely long cylindrical pipe are investigated numerically by solving an eigenvalue problem. To avoid unphysical reflections at the finite grid boundaries placed in the uniform cross-sections of the pipe, perfectly matched layer absorbing boundary conditions are applied in the form of the complex scaling method of atomic and molecular physics. Examples of the structures investigated are sound-hard spheres, cylinders, cavities and closed side branches. Several truly trapped modes with zero radiation loss are identified for frequencies below the first cutoff frequency of the pipe. Such trapped modes can be excited aerodynamically by coherent vortices if the frequency of the shed vortices is close to a resonant frequency. Furthermore, numerical evidence is presented for the existence of isolated embedded trapped modes for annular cavities above the first cutoff frequency and for closed side branches below the first cutoff frequency. As applications of engineering interest, the acoustic resonances are computed for a ball-type valve and around a simple model of a high-speed train in an infinitely long tunnel.

Acoustic resonances and trapped modes in annular plate cascades

2009 ◽  
Vol 628 ◽  
pp. 155-180 ◽  
Author(s):  
WERNER KOCH
Keyword(s):  
Axial Flow ◽  
Radiation Condition ◽  
Absorbing Boundary Conditions ◽  
Radiation Damping ◽  
Resonance Problem ◽  
Trapped Modes ◽  
Mean Flow ◽  
Absorbing Boundary ◽  
Complex Scaling Method ◽  
Acoustic Resonances

As a stepping stone towards understanding acoustic resonances in axial flow compressors, acoustic resonances are computed numerically in fixed single and tandem plate cascades in an infinitely long annular duct. Applying perfectly matched layer absorbing boundary conditions in the form of the complex scaling method of atomic and molecular physics to approximate the radiation condition the resonance problem is transformed into an eigenvalue problem. Of particular interest are resonances with zero radiation damping (trapped modes) or very small radiation damping (nearly trapped modes). Such resonances can be excited by wakes from compressor cascades or struts. If the shedding frequency is sufficiently close to an acoustic resonant frequency, the latter may control the vortex shedding causing high-intensity tonal noise or occasionally even blade failure. All resonances are computed for zero mean flow approximating low-Mach-number flows. The influence of various cascade parameters on the resonant frequencies is studied and, whenever possible, our numerical results are compared with published experimental findings.

Acoustic resonances in a high-lift configuration

2007 ◽  
Vol 582 ◽  
pp. 179-202 ◽  
Author(s):  
STEFAN HEIN ◽  
THORSTEN HOHAGE ◽  
WERNER KOCH ◽  
JOACHIM SCHÖBERL
Keyword(s):  
Leading Edge ◽  
Absorbing Boundary Conditions ◽  
Computational Domain ◽  
Mean Flow ◽  
Coherent Noise ◽  
Absorbing Boundary ◽  
High Lift ◽  
Complex Scaling Method ◽  
Temporal Decay ◽  
Acoustic Resonances

Low- and high-frequency acoustic resonances are computed numerically via a high-order finite-element code for a generic two-dimensional high-lift configuration with a leading-edge slat. Zero mean flow is assumed, approximating the low-Mach-number situation at aircraft landing and approach. To avoid unphysical reflections at the boundaries of the truncated computational domain, perfectly matched layer absorbing boundary conditions are implemented in the form of the complex scaling method of atomic and molecular physics. It is shown that two types of resonance exist: resonances of surface waves which scale with the total airfoil length and longitudinal cavity-type resonances which scale with the slat cove length. Minima exist in the temporal decay rate which can be associated with the slat cove resonances and depend on the slat cove geometry. All resonances are damped owing to radiation losses. However, if coherent noise sources exist, as observed in low-Reynolds-number experiments, these sources can be enhanced acoustically by the above resonances if the source frequency is close to a resonant frequency.

Towards a General-Purpose Open Boundary Condition for Wave Simulations

2011 ◽  
Author(s):  
Bulent Duz ◽  
Rene H. M. Huijsmans ◽  
Peter R. Wellens ◽  
Mart J. A. Borsboom ◽  
Arthur E. P. Veldman
Keyword(s):  
Boundary Condition ◽  
Three Dimensional ◽  
General Purpose ◽  
Absorbing Boundary Conditions ◽  
Design Stage ◽  
Open Boundary ◽  
Computational Domain ◽  
Absorbing Boundary ◽  
Scaled Model ◽  
Artificial Boundaries

For the design of FPSO’s in harsh environments an accurate assessment of the ability of the platform to survive in extreme sea conditions is of prime importance. Next to scaled model tests on the FPSO in waves also CFD capabilities are at the disposal of the designer. However even with the fastest computers available it is still a challenge to use CFD in the design stage because of the large computational resources they require. In that respect to use a small computational domain will improve the turn around time of the computations, however at the expense of various numerical artifacts, like reflection on artificial boundaries in the computational domain. In order to mitigate the reflection properties new absorbing boundary conditions have been developed. The work in this paper is constructed on the previous study about the generating and absorbing boundary condition (GABC) in the ComFLOW project. We present a method to apply the GABC on all the boundaries in a three dimensional domain. The implementation of the GABC in ComFLOW is explained in detail.

A NONCONFORMING MIXED FINITE ELEMENT METHOD FOR MAXWELL'S EQUATIONS

2000 ◽  
Vol 10 (04) ◽  
pp. 593-613 ◽  
Author(s):  
JIM DOUGLAS ◽  
JUAN E. SANTOS ◽  
DONGWOO SHEEN
Keyword(s):  
Finite Element ◽  
Mixed Method ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Mixed Finite Element ◽  
Three Dimensional ◽  
Mixed Finite Element Method ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
Three Dimensional Models

We present a nonconforming mixed finite element scheme for the approximate solution of the time-harmonic Maxwell's equations in a three-dimensional, bounded domain with absorbing boundary conditions on artificial boundaries. The numerical procedures are employed to solve the direct problem in magnetotellurics consisting in determining a scattered electromagnetic field in a model of the earth having bounded conductivity anomalies of arbitrary shapes. A domain-decomposition iterative algorithm which is naturally parallelizable and is based on a hybridization of the mixed method allows the solution of large three-dimensional models. Convergence of the approximation by the mixed method is proved, as well as the convergence of the iteration.

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